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REVIEW 3 major objections 3 minor 58 references

Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification

T0 review · 3 major / 3 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A compiler that treats every Pauli term in one global tableau cuts two-qubit gates by 59% and circuit depth by 91% on average.

desk verdict Novel holistic BSF compiler with a likely semantic bug in the weight-2 emission step; the headline numbers may not be for the same unitary. read the letter →

arxiv 2608.11579 v1 pith:6PUX7PUW submitted 2026-08-12 quant-ph

Zhaohui Yang , Yuwei Han , Ruiyun Zhang , Dawei Ding , Jianxin Chen , Yuan Feng , Yuan Xie This is my paper · ORCID
classification quant-ph
keywords HamiltoniansimulationPauliexponentialsbinarysymplecticformCliffordgatesquantumcircuitcompilationtwo-qubitgatecountdepthvariationalalgorithms
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper sets out to establish that compiling a Hamiltonian simulation program, expressed as a sequence of Pauli-rotation exponentials, can be done far more effectively by keeping the entire sequence in a single global binary symplectic tableau and applying controlled-Pauli Clifford gates to the whole tableau at once, rather than diagonalizing or grouping terms. On a 100-program benchmark suite it reports average reductions of 59% in two-qubit gate count and 91% in two-qubit circuit depth relative to naive term-by-term synthesis, with better aggregate results than six prior compilers. The claimed mechanism is simultaneous weight reduction across all Pauli rows, an adaptive rule that emits weight-two two-qubit blocks only when the remaining tableau is sparse, and a causality-preserving scheduler that rearranges emitted blocks for parallelism. If true, this would mean that the global algebraic structure of Pauli exponentials, not just local gate cancellation, is the main handle for optimizing Hamiltonian simulation circuits.

What carries the argument

The load-bearing object is the binary symplectic form tableau, an m by 2n binary matrix encoding m Pauli strings on n qubits, together with the universal controlled gate family C(P,Q), CNOT-equivalent Clifford gates with Pauli axes P and Q in {X, Y, Z} that update four tableau columns but act on every row simultaneously. This representation lets support, weight, overlap, and commutation be computed by F2-linear arithmetic, so a greedy Clifford search can be scored globally in polynomial time. The adaptive emission rule, emitting weight-one rows unconditionally and weight-two blocks only when the average residual density rho_A falls below rho = 0.35, prevents collateral inflation of unresolved rows. The as-soon-as-possible scheduler, inspired by graph edge-coloring, applies the paper's two commutation propositions to pull blocks earlier without violating the forward Clifford frame. The interaction-rank criterion, showing that an exact two-qubit Pauli-evolution block needs at most two CNOTs whenever its interaction matrix has rank at most two, justifies emitting weight-two blocks cheaply.

What would settle it

Run the same 100 benchmarking Hamiltonians with only weight-one emission (the rho = 0 endpoint) and with unconditional weight-two emission (the rho = 1 endpoint): if either endpoint matches or beats the default rho = 0.35 configuration in aggregate two-qubit gate count and depth, the paper's claim that adaptive density-based emission is necessary would be falsified.

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Extended reading notes

Core claim

The central claim is that grouping-free, holistic tableau simplification strictly outperforms prior Pauli-intermediate-representation compilers in both gate count and depth. Symphony maintains all Pauli strings as rows of the binary symplectic form tableau; at each step it picks the lowest-weight active row and searches the nine CNOT-equivalent controlled-Pauli Clifford gates (the universal controlled gates) acting on its support qubits, scoring each candidate by its effect on the whole tableau through total weight decrease, number of rows reduced, and number of rows inflated. Once a row reaches weight one it is emitted as a single-qubit rotation; weight-two rows are emitted as two-qubit blocks only when the average residual tableau density falls below a threshold rho = 0.35. The emitted stream is then rescheduled by an as-soon-as-possible heuristic that uses exact commutation rules for controlled-Pauli gates and Pauli rotations to preserve causal precedences while exposing parallelism. The paper reports geometric-mean optimization rates of 0.411 in two-qubit gate count and 0.09 in two-qubit depth on the benchmark suite, corresponding to the 59% and 91% reductions.

Load-bearing premise

The headline numbers depend on a density threshold, set to 0.35, that decides when weight-two two-qubit blocks may be emitted instead of being simplified further, and the paper's ablation shows strong sensitivity to this threshold while also recommending it be swept per instance, so the reported averages assume the threshold can be chosen well for each workload.

Editorial extensions

If this is right

  • Pauli-exponential workloads can be compiled with polynomial worst-case overhead, O(m^2 n^3), while matching or beating compilers that rely on long-horizon searches.
  • Because two-qubit depth is reduced across every benchmark family, the block parallelism exposed by the scheduler is a consistent, not incidental, source of gain.
  • For expectation-value workloads, the terminal Clifford sequence can be absorbed into measurement observables, removing part of the output circuit entirely.
  • The logical-level advantage persists on limited-connectivity hardware: the paper reports lower two-qubit depth than all baselines even on a heavy-hex topology, despite larger routing overhead than topology-aware compilers.
  • In the early fault-tolerant regime, T-count stays roughly compiler-invariant while T-depth is reduced by a factor of up to 2.73x over one baseline, so the depth improvement carries over to non-Clifford rotation schedules.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The method's reliance on global algebraic structure suggests it should transfer to fermionic encodings with irregular locality, such as Bravyi-Kitaev tree encodings, where cross-group correlations are abundant; this is a testable extension beyond the paper's chemistry and spin-model instances.
  • The density threshold rho is a per-instance tuning knob, and the paper's own ablation implies the reported averages come from a best-of-sweep policy rather than one fixed pre-registered setting, which is worth keeping in mind when comparing against fixed-strategy compilers.
  • The interaction-rank criterion for two-qubit Pauli-evolution blocks could be used outside compilation, for example as a cheap analytic substitute for numerical KAK decomposition in other circuit-synthesis contexts.
  • The exact local commutation tests for controlled-Pauli gates and Pauli rotations could be adopted by other peephole optimizers as a way to reorder Clifford and rotation operations without building a full dependency graph.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper introduces Symphony, a compiler for Hamiltonian-simulation workloads expressed as Pauli-IR sequences. Symphony represents all Pauli exponentials in a global binary symplectic form (BSF) tableau and iteratively applies controlled-Pauli Clifford conjugations to reduce row weights, adaptively emitting weight-1 and weight-2 rows as blocks, followed by a causality-preserving ASAP block scheduler. The authors report average reductions of 59% in two-qubit gate count and 91% in two-qubit depth on 100 HamLib benchmarks plus scaled UCCSD workloads, and claim that Symphony strictly Pareto-dominates six prior compilers, with 1.14-1.58x fewer two-qubit gates and 1.87-5.67x shallower depth.

Significance. The holistic BSF simplification framework, the adaptive two-qubit block emission idea, and the commutativity-aware scheduling are potentially valuable contributions to quantum circuit compilation for Pauli-IR workloads. The algebraic lemmas (Theorem 3.1, Propositions 4.1 and 4.2) are sound, the complexity analysis is explicit, and the empirical scope is broad. If the semantic-correctness issue identified below is resolved and the empirical claims are restated accurately, the work would be of substantial interest to the quantum compilation community.

major comments (3)
  1. [Algorithm 1, lines 20-29; Theorem 3.1] The Emit function retires all rows with weight at most two into a single emitted block E_l without checking whether the rows commute or share the same qubit pair. Theorem 3.1 applies only to an exact two-qubit unitary exp(-i H_J) for a single pair's interaction matrix H_J = sum J_mu_nu sigma_mu tensor sigma_nu. A product of rotations prod exp(-i theta P) is not equal to exp(-i sum theta P) when the Pauli rows do not commute, and rows on different qubit pairs cannot be represented by a 3x3 interaction matrix at all. The paper therefore does not establish that the emitted block implements the input Pauli-IR semantics, and the reported gate-count and depth reductions in Tables 3-4 and Figures 6-7 may be comparing circuits that implement different unitaries. Appendix B, Lemma B.1 bounds only the first commutator and does not close this gap. The authors should either add an explicit commutation and same-pair check before grouping rows into a block, or implement each block as a product of individual rotations and re-derive the cost model accordingly, and then rerun the evaluation.
  2. [Abstract; Section 5.2] The abstract's claim that Symphony 'strictly Pareto-dominates prior state-of-the-art compilers' is contradicted by the paper's own data in Section 5.2, which acknowledges that Paulihedral retains marginal gate-count advantages on binary and discrete optimization workloads. Strict Pareto dominance is a strong per-instance statement and is not supported by the reported aggregate or category-level results. The claim should be weakened to aggregate dominance or restated as separate per-metric improvements.
  3. [Table 5; Section 5.5.1] The reported headline reductions depend on the density threshold rho, and the ablation in Table 5 shows strong sensitivity: rho = 0 degrades aggregate two-qubit depth by 112.5% and rho = 1 degrades aggregate gate count by 8.8% and chemistry gate count by 27.9%. Since Section 5.5.1 suggests sweeping rho in parallel to select the optimal value, the published aggregate numbers may be based on per-instance or per-category selection after seeing the data rather than on a fixed, pre-specified policy. The authors should report the exact rho choices used for each instance or category, or adopt a validation protocol such as cross-validation, before presenting the 59% and 91% reductions as the performance of a single compiler configuration.
minor comments (3)
  1. [Section 3.3] The phrase 'an two-qubit Pauli-evolution block' contains a typo and should be 'a two-qubit Pauli-evolution block'.
  2. [Section 2.3] The equivalence formula for C(P,Q) in terms of single-qubit Cliffords and CNOT appears twice in nearly identical form; one copy should be removed to avoid duplication.
  3. [Section 5.4] The statement that the non-Clifford rotation count requires 'a median of 102.5 T gates per rotation' is unclear: the median T-gate cost is an artifact of the GridSynth approximation at precision 10^-10, not an intrinsic property of the Hamiltonian, and should be worded accordingly.

Circularity Check

0 steps flagged · score 2.0 of 10

No substantive circularity; the core BSF-simplification claims are measured against external HamLib benchmarks and the supporting theorems are proved in-text.

full rationale

Symphony's central claim—that global BSF simplification plus adaptive emission plus causality-preserving scheduling reduces two-qubit gate count and depth—is an empirical result evaluated on the external HamLib suite and UCCSD workloads. The algebraic engine (Algorithm 1) is self-contained: UCG update rules are derived in Appendix A, and Theorem 3.1's interaction-rank criterion is proved in Appendix B via SVD/Cartan reduction; it does not presuppose the benchmark outcomes. The rho emission threshold is a fixed design hyperparameter (rho=0.35) with an ablation (Table 5); the sentence about sweeping rho in parallel is a practical suggestion, not a report of tuned results, so the headline numbers are not a fit renamed as prediction. Self-citations to Phoenix [50], Paulihedral [24], and the authors' routing work [51] are prior-work comparisons and are not used to justify the uniqueness or correctness of the simplification steps. One genuine concern is semantic rather than circular: grouping noncommuting weight-2 rows into a single emitted block is justified by Theorem 3.1, which bounds exp(-iH_J), while the input Pauli-IR is a product of rotations; if the rows do not commute, the block may not implement the required unitary. This is a correctness risk, not a circular derivation, and is outside the scope of this pass.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central empirical claims rest on a tuned hyperparameter (rho) and on standard background theory (KAK decomposition, Pauli algebra, Clifford group generation). No new physical entities are introduced. The core algorithmic components, BSF tableau, UCG, and greedy selection, are adapted from cited prior work; the contribution is the specific holistic combination and the scheduling.

free parameters (2)
  • density threshold rho = 0.35 (default)
    Controls when weight-2 Pauli rows are emitted as blocks (Algorithm 1, lines 24-26). Tuned on the HamLib suite; the ablation shows strong sensitivity, and the paper suggests sweeping rho per instance, making the reported numbers data-selected.
  • greedy benefit weights beta = (-Delta W, N-, -N+) = lexicographic ranking
    Hand-designed heuristic to rank Clifford candidates (Algorithm 1, lines 9-13). Not fitted numerically, but an arbitrary design choice that affects results.
assumptions (5)
  • standard math Pauli commutation is captured by the binary symplectic inner product
    Used pervasively, including Eq. (5) in Section 2.2 and the commutation tests in the scheduler.
  • standard math KAK/Cartan decomposition of SU(4): rank(J) <= 2 implies at most 2 CNOTs for a two-qubit Pauli-evolution block
    Theorem 3.1 and Appendix B; an established result in two-qubit synthesis theory, used to justify emitting weight-2 blocks.
  • domain assumption The compiler may reorder Pauli exponentials within a simulation step subject to commutation
    Section 2.1 states admissible ordering depends on front-end semantics; the scheduler relies on this freedom for the depth reductions.
  • standard math The nine UCG gates generate the two-qubit Clifford group
    Section 2.3 cites Grier and Schaeffer [17]; the basis for using UCGs as simplification primitives.
  • domain assumption Two-qubit gate count and depth are the correct primary cost model, with single-qubit gates ignored
    Section 5.1.3; reasonable for NISQ comparisons but it omits T-count from the main gate-count claims.

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Pith. "Pith review of Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification." pith.science (2026). https://pith.science/paper/6PUX7PUW

@misc{pith2026260811579,
  author       = {Pith},
  title        = {Pith review of: Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6PUX7PUW}},
  note         = {Machine review of arXiv:2608.11579}
}
abstract

Hamiltonian simulation is a core quantum workload, underpinning variational quantum algorithms and Trotterized time evolution. Such programs are expressed as Pauli exponential sequences, exhibiting structural patterns that are highly amenable to high-level synthesis and optimization. Existing compilers, however, fail to fully unlock the optimization potential of their global algebraic structure, even when employing advanced graph- or tableau-based methods. We present Symphony, a holistic compilation approach built on the binary symplectic form (BSF) representation of Pauli strings. Unlike prior group-wise BSF simplification and path-based Pauli network synthesis, Symphony applies generalized controlled-Pauli Clifford transformations directly to a global BSF tableau, adaptively reducing active Pauli rows and emitting eligible two-qubit blocks other than single-qubit rotations in a forward Clifford frame. Following algebraic simplification, Symphony performs a causality-preserving block rescheduling heuristic that respects frame-induced dependencies while exposing extensive two-qubit block parallelism opportunities. This streamlined compilation style comprehensively exploits simultaneous simplification and commutativity opportunities, achieving efficient global optimization without relying on computationally expensive heuristics or long-horizon searches. Across the generic Hamiltonian simulation benchmarks in HamLib, Symphony achieves average reductions of 59% in two-qubit gate count and 91% in circuit depth. It strictly Pareto-dominates prior state-of-the-art compilers, requiring 1.14--1.58$\times$ fewer two-qubit gates and especially shrinking two-qubit circuit depth by a substantial factor of 1.87--5.67$\times$ on average.

Figures

Figures reproduced from arXiv: 2608.11579 by the authors.

Figure 1
Figure 1. (a) Naïve synthesis vs. (b) simultaneous simplifica￾tion of Pauli exponentials. weight-𝑤 Pauli exponential requires 2(𝑤 − 1) CNOT gates for synthesis [36]. However, a naïve, term-by-term synthesis inherently ignores the global algebraic commonalities of the Hamiltonian. It forces the circuit to repeatedly compute and uncompute overlapping parity structures rather than lever￾aging the shared relationships across the … view at source ↗
Figure 2
Figure 2. Example of BSF update by Clifford transformation. simulation step; exact commutation constraints are retained when required by the input semantics. 2.2 Binary Symplectic Form of Pauli-IRs Symphony represents Pauli operators in a high-level, formal binary symplectic form (BSF) tableau [1, 32]. Given 𝑚 Pauli rotations on 𝑛 qubits, their operators are encoded as 𝑇 = [𝑋 | 𝑍] ∈ F 𝑚×2𝑛 2 , (2) where the 𝑖-th row encodes P… view at source ↗
Figure 3
Figure 3. illustrates this loss concretely: the four heteroge￾neously supported strings share exploitable structure that spans the imposed group boundaries, and processing them without grouping halves the number of required two-qubit Clifford conjugations. In real-world applications, cross-group optimization opportunities are ubiquitous. For example, in chemistry simulations, Jordan-Wigner (JW) encodings char￾acteristically y… view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Avoiding degradation via early two-qubit block emission during BSF simplification (𝑋, 𝑌, 𝑍 shown as red, green, blue). (a) Initial Pauli strings to be simplified by Clif￾ford conjugation acting on (𝑞0, 𝑞1). (b) Forcing target 𝑃1 to weight-1 invariably inflates the weig…
Figure 5
Figure 5. Figure 5: Overview of the Symphony compilation workflow. are ranked by the quantified benefit 𝛽 = (−Δ𝑊 , 𝑁−, −𝑁+). This metric explicitly incentivizes simultaneous simplifica￾tion: it prioritizes the UCG that induces the steepest drop in total tableau weight, breaking ties by fa…
Figure 6
Figure 6. Figure 6: Pairwise comparison of Symphony against six SOTA baselines on the 100-program HamLib benchmark suite. The dashed diagonal line denotes equal performance; points above it favor Symphony; shaded diagonal bands serve as multiplicative-ratio guides (1–1.5×, 1.5–2×, 2–3×, 3…
Figure 7
Figure 7. Figure 7: Per-program𝑇 -depth of each baseline compared to Symphony across HamLib. The dashed diagonal represents equal 𝑇 -depth; points above it favor Symphony; shaded re￾gions indicate multiplicative-ratio bounds (1–1.5×, 1.5–2×, 2–3×, 3–5×, and 5–10×) [PITH_FULL_IMAGE:figure…
Figure 8
Figure 8. Figure 8: Compilation latency comparison. Solid lines de￾note end-to-end compilers generating equivalent circuits, whereas dashed lines represent non-end-to-end baselines (Paulihedral and Tetris) that only process Pauli strings. exhibits a latency scaling curve that closely alig…

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Works this paper leans on

58 extracted references · 47 canonical work pages

  1. [1]

    Scott Aaronson and Daniel Gottesman. 2004. Improved Simulation of Stabilizer Circuits.Physical Review A70, 5 (2004), 052328

    work page 2004

  2. [2]

    Egger, Bruce G

    Amira Abbas, Andris Ambainis, Brandon Augustino, Andreas Bärtschi, Harry Buhrman, Carleton Coffrin, Giorgio Cortiana, Vedran Dunjko, Daniel J. Egger, Bruce G. Elmegreen, Nicola Franco, Filippo Fratini, Bryce Fuller, Julien Gacon, Constantin Gonciulea, Sander Gribling, Swati Gupta, Stuart Hadfield, Raoul Heese, Gerhard Kircher, Thomas Kleinert, Thorsten Ko...

    work page 2024

  3. [3]

    Brown, Giuseppe Carleo, Lincoln D

    Ehud Altman, Kenneth R. Brown, Giuseppe Carleo, Lincoln D. Carr, Eugene Demler, Cheng Chin, Brian DeMarco, Sophia E. Economou, Mark A. Eriksson, Kai-Mei C. Fu, Markus Greiner, Kaden R. A. Haz- zard, Randall G. Hulet, Alicia J. Kollár, Benjamin L. Lev, Mikhail D. Lukin, Ruichao Ma, Xiao Mi, Shashank Misra, Christopher Monroe, Kater Murch, Zaira Nazario, Ka...

    work page 2021

  4. [4]

    Matthew Amy, Dmitri Maslov, Michele Mosca, and Martin Roetteler

    work page

  5. [5]

    Bela Bauer, Sergey Bravyi, Mario Motta, and Garnet Kin-Lic Chan

    work page

  6. [6]

    Sergey Bravyi and Alexei Kitaev. 2005. Universal quantum computa- tion with ideal Clifford gates and noisy ancillas.Physical Review A71, 2 (2005), 022316

    work page 2005

  7. [7]

    Sergey Bravyi and Dmitri Maslov. 2021. Hadamard-Free Circuits Expose the Structure of the Clifford Group.IEEE Transactions on Information Theory67, 7 (2021), 4546–4563

    work page 2021

  8. [8]

    Olson, Matthias Degroote, Peter D

    Yudong Cao, Jonathan Romero, Jonathan P. Olson, Matthias Degroote, Peter D. Johnson, Mária Kieferová, Ian D. Kivlichan, Tim Menke, Borja Peropadre, Nicolas P. D. Sawaya, Sukin Sim, Libor Veis, and Alán Aspuru-Guzik. 2019. Quantum chemistry in the age of quantum computing.Chemical Reviews119, 19 (2019), 10856–10915

    work page 2019

Show all 58 references
  1. [9]

    Childs, Dmitri Maslov, Yunseong Nam, Neil J

    Andrew M. Childs, Dmitri Maslov, Yunseong Nam, Neil J. Ross, and Yuan Su. 2018. Toward the first quantum simulation with quantum speedup.Proceedings of the National Academy of Sciences115, 38 (2018), 9456–9461

    2018

  2. [10]

    Alexander Cowtan, Silas Dilkes, Ross Duncan, Will Simmons, and Seyon Sivarajah. 2019. Phase gadget synthesis for shallow circuits. InProceedings 16th International Conference on Quantum Physics and Logic, Vol. 318. Open Publishing Association, 213–228

    2019

  3. [11]

    Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bi- enias, Chi-Fang Chen, András Gilyén, Connor T

    Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bi- enias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brandão. 2025.Quantum algo- rithms: A survey of...

    2025

  4. [12]

    Ayushi Dubal, David Kremer, Simon Martiel, Victor Villar, Derek Wang, and Juan Cruz-Benito. 2025. Pauli Network Circuit Synthesis with Reinforcement Learning.arXiv preprint arXiv:2503.14448(2025)

    2025 arXiv

  5. [13]

    Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. 2014. A quantum approximate optimization algorithm.arXiv preprint arXiv:1411.4028 (2014)

    2014 arXiv

  6. [14]

    Richard P Feynman. 1982. Simulating physics with computers.Inter- national journal of theoretical physics21, 6 (1982), 467–488

    1982

  7. [15]

    I. M. Georgescu, S. Ashhab, and Franco Nori. 2014. Quantum simula- tion.Reviews of Modern Physics86, 1 (2014), 153–185

    2014

  8. [16]

    Timothée Goubault de Brugière and Simon Martiel. 2024. Faster and shorter synthesis of Hamiltonian simulation circuits.arXiv preprint arXiv:2404.03280(2024)

    2024 arXiv

  9. [17]

    Daniel Grier and Luke Schaeffer. 2022. The Classification of Clifford Gates over Qubits.Quantum6 (2022), 734

    2022

  10. [18]

    Aram W Harrow, Avinatan Hassidim, and Seth Lloyd. 2009. Quantum algorithm for linear systems of equations.Physical review letters103, 15 (2009), 150502

    2009

  11. [19]

    Yuwei Jin, Zirui Li, Fei Hua, Tianyi Hao, Huiyang Zhou, Yipeng Huang, and Eddy Z Zhang. 2024. Tetris: A Compilation Framework for VQA Applications in Quantum Computing. In2024 ACM/IEEE 51st Annual International Symposium on Computer Architecture (ISCA). IEEE, 277– 292

    2024

  12. [20]

    Aleks Kissinger and Arianne Meijer-van de Griend. 2020. CNOT circuit extraction for topologically-constrained quantum memories. Quantum Information and Computation20, 7&8 (2020), 581–596

    2020

  13. [21]

    Yi-Hsiang Kuo, Hsiang-Chun Yang, Hsin-Yu Chen, and Chung- Yang Ric Huang. 2026. Unified Pauli-Rotation Synthesis for Relieving CX-Count Overhead in Tableau-Based Quantum Circuit Optimization Flow. In2026 Design, Automation & Test in Europe Conference (DATE). IEEE, 1–7

    2026

  14. [22]

    Lingling Lao and Dan E Browne. 2022. 2qan: A quantum compiler for 2-local qubit hamiltonian simulation algorithms. InProceedings of the 49th Annual International Symposium on Computer Architecture. 351–365

    2022

  15. [23]

    Gushu Li, Yufei Ding, and Yuan Xie. 2019. Tackling the qubit map- ping problem for NISQ-era quantum devices. InProceedings of the twenty-fourth international conference on architectural support for pro- gramming languages and operating systems. 1001–1014

    2019

  16. [24]

    Gushu Li, Anbang Wu, Yunong Shi, Ali Javadi-Abhari, Yufei Ding, and Yuan Xie. 2022. Paulihedral: a generalized block-wise compiler opti- mization framework for quantum simulation kernels. InProceedings of the 27th ACM International Conference on Architectural Support for Progr...

    2022

  17. [25]

    Yongshang Li, Yu Zhang, Haoning Deng, Mingyu Chen, and Zhenyu Li

  18. [26]

    Daniel Litinski. 2019. A game of surface codes: Large-scale quantum computing with lattice surgery.Quantum3 (2019), 128. 12 Efficient Compilation for Hamiltonian Simulation via Global Binary Symplectic Form Simplification

    2019

  19. [27]

    Daniel Litinski. 2019. Magic state distillation: Not as costly as you think.Quantum3 (2019), 205

    2019

  20. [28]

    Ji Liu, Alvin Gonzales, Benchen Huang, Zain Hamid Saleem, and Paul D Hovland. 2025. QuCLEAR: Clifford Extraction and Absorp- tion for Quantum Circuit Optimization. In2025 IEEE International Symposium on High Performance Computer Architecture (HPCA). IEEE, 158–172

    2025

  21. [29]

    Seth Lloyd. 1996. Universal quantum simulators.Science273, 5278 (1996), 1073–1078

    1996

  22. [30]

    Guang Hao Low and Isaac L. Chuang. 2019. Hamiltonian simulation by qubitization.Quantum3 (2019), 163

    2019

  23. [31]

    Mulundano Machiya, Matt Menickelly, Paul Hovland, and Ji Liu. 2026. MonteQ: A Monte Carlo Tree Search Based Quantum Circuit Synthesis Framework. InISC High Performance 2026 Research Paper Proceedings (41st International Conference). IEEE, 1–12

    2026

  24. [32]

    Dmitri Maslov and Martin Roetteler. 2018. Shorter Stabilizer Circuits via Bruhat Decomposition and Quantum Circuit Transformations. IEEE Transactions on Information Theory64, 7 (2018), 4729–4738

    2018

  25. [33]

    Benjamin, and Xiao Yuan

    Sam McArdle, Suguru Endo, Alán Aspuru-Guzik, Simon C. Benjamin, and Xiao Yuan. 2020. Quantum computational chemistry.Reviews of Modern Physics92, 1 (2020), 015003

    2020

  26. [34]

    Priyanka Mukhopadhyay, Nathan Wiebe, and Hong Tao Zhang. 2023. Synthesizing efficient circuits for Hamiltonian simulation.npj Quan- tum Information9, 1 (2023), 31

    2023

  27. [35]

    Nation, Abdullah Ash Saki, Sebastian Brandhofer, Luciano Bello, Shelly Garion, Matthew Treinish, and Ali Javadi-Abhari

    Paul D. Nation, Abdullah Ash Saki, Sebastian Brandhofer, Luciano Bello, Shelly Garion, Matthew Treinish, and Ali Javadi-Abhari. 2025. Benchmarking the performance of quantum computing software for quantum circuit creation, manipulation and compilation.Nature Com- putational Sc...

    2025

  28. [36]

    2010.Quantum computation and quantum information

    Michael A Nielsen and Isaac L Chuang. 2010.Quantum computation and quantum information. Cambridge university press

    2010

  29. [37]

    Jennifer Paykin, Albert T Schmitz, Mohannad Ibrahim, Xin-Chuan Wu, and Anne Y Matsuura. 2023. PCOAST: a Pauli-based quantum circuit optimization framework. In2023 IEEE International Conference on Quantum Computing and Engineering (QCE), Vol. 1. IEEE, 715–726

    2023

  30. [38]

    Alberto Peruzzo, Jarrod McClean, Peter Shadbolt, Man-Hong Yung, Xiao-Qi Zhou, Peter J Love, Alán Aspuru-Guzik, and Jeremy L O’brien

  31. [39]

    McClean, Cornelius Hempel, Peter J

    Jonathan Romero, Ryan Babbush, Jarrod R. McClean, Cornelius Hempel, Peter J. Love, and Alán Aspuru-Guzik. 2018. Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz.Quantum Science and Technology4, 1 (2018), 014008

    2018

  32. [40]

    Ross and Peter Selinger

    Neil J. Ross and Peter Selinger. 2016. Optimal ancilla-free Clifford+T approximation of z-rotations.Quantum Information & Computation 16, 11–12 (2016), 901–953

    2016

  33. [41]

    Nicolas PD Sawaya, Daniel Marti-Dafcik, Yang Ho, Daniel P Ta- bor, David E Bernal Neira, Alicia B Magann, Shavindra Premaratne, Pradeep Dubey, Anne Matsuura, Nathan Bishop, Wibe A de Jong, Simon Benjamin, Ojas Parekh, Norm Tubman, Katherine Klymko, and Daan Camps. 2024. HamLib...

    2024

  34. [42]

    Albert T Schmitz, Nicolas P D Sawaya, Sonika Johri, and A Y Matsuura

  35. [43]

    Peter W Shor. 1994. Algorithms for quantum computation: discrete logarithms and factoring. InProceedings 35th annual symposium on foundations of computer science. Ieee, 124–134

    1994

  36. [44]

    Yuan Su, Dominic W Berry, Nathan Wiebe, Nicholas Rubin, and Ryan Babbush. 2021. Fault-tolerant quantum simulations of chemistry in first quantization.PRX Quantum2, 4 (2021), 040332

    2021

  37. [45]

    Masuo Suzuki. 1990. Fractal decomposition of exponential operators with applications to many-body theories and Monte Carlo simulations. Physics Letters A146, 6 (1990), 319–323

    1990

  38. [46]

    Teague Tomesh, Kaiwen Gui, Pranav Gokhale, Yunong Shi, Frederic T Chong, Margaret Martonosi, and Martin Suchara. 2021. Optimized quantum program execution ordering to mitigate errors in simulations of quantum systems. In2021 IEEE International Conference on Rebooting Computing...

    2021

  39. [47]

    H. F. Trotter. 1959. On the product of semi-groups of operators.Proc. Amer. Math. Soc.10, 4 (1959), 545–551

    1959

  40. [48]

    Ewout Van Den Berg and Kristan Temme. 2020. Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters.Quantum4 (2020), 322

    2020

  41. [49]

    Vivien Vandaele, Simon Martiel, and Timothée Goubault de Brugière

  42. [50]

    Zhaohui Yang, Dawei Ding, Chenghong Zhu, Jianxin Chen, and Yuan Xie. 2025. PHOENIX: Pauli-Based High-Level Optimization Engine for Instruction Execution on NISQ Devices. In2025 62nd ACM/IEEE Design Automation Conference (DAC). IEEE, 1–7

    2025

  43. [51]

    Zhaohui Yang, Kai Zhang, Xinyang Tian, Xiangyu Ren, Yingjian Liu, Yunfeng Li, Dawei Ding, Jianxin Chen, and Yuan Xie. 2026. Unifying qubit routing across diverse quantum isas via canonical representation. In2026 ACM/IEEE 53rd Annual International Symposium on Computer Architec...

    2026

  44. [52]

    Henry Zou, Matthew Treinish, Kevin Hartman, Alexander Ivrii, and Jake Lishman. 2024. LightSABRE: A Lightweight and Enhanced SABRE Algorithm.arXiv preprint arXiv:2409.08368(2024). A Clifford formalism based on Universal Controlled Gate A.1 Generalized CNOT Gate Definition We de...

    2024 arXiv

  45. [2013]

    A meet-in-the-middle algorithm for fast synthesis of depth- optimal quantum circuits.IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems32, 6 (2013), 818–830

    2013

  46. [2014]

    Nature communications5, 1 (2014), 4213

    A variational eigenvalue solver on a photonic quantum processor. Nature communications5, 1 (2014), 4213

    2014

  47. [2020]

    Quantum algorithms for quantum chemistry and quantum materials science.Chemical Reviews120, 22 (2020), 12685–12717

    2020

  48. [2022]

    Phase polynomials synthesis algorithms for NISQ architectures and beyond.Quantum Science & Technology7, 4 (2022), 045027

    2022

  49. [2024]

    Graph optimization perspective for low-depth Trotter-Suzuki decomposition.Physical Review A109, 4 (2024), 042418

    2024

  50. [2025]

    PauliForest: Connectivity-Aware Synthesis and Pauli-Oriented Qubit Mapping for Near-Term Quantum Simulation.IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems44, 6 (2025), 2119–2129

    2025

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